Question

Graph the following piecewise function and then find the range.

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

The given piecewise function is

$f(x)=\begin{cases}3x^2+1 & \text{ if } -4$

Range is the set of output or y values.

The given function for 6 ≤ x < 9 is

$f(x)=6$

It is a constant function, the value of function is 6 for all values of x.

Range = 6

The given function for -4 < x < 6 is

$f(x)=3x^2+1$          .... (1)

It is a quadratic function.

The vertex form of a quadratic function is

$f(x)=a(x-h)^2+k$         ....(2)

Where (h,k) is vertex and a is constant.

From (1) and (2), we get a=3,h=0,k=1.

The vertex of this function is (0,1), it means the range of this function is greater than or equal to 1. But this function is only defined for -4 < x < 6.

$f(-4)=3(-4)^2+1=49$

$f(6)=3(6)^2+1=109$

The maximum value of the maximum value of the function is 109 at x=6. Since 6 is not included in the interval -4 < x < 6, therefore 109 is not included in the range.

Range = [1,109)

When we combined the range of both functions we get

Range = [1,109)

Therefore the correct option is 3.

Answer 2

The same function as in the one of other your questions.

$D:[1,109)$